Conformers of formic acid (FA) are studied by IR spectroscopy in solid hydrogen. The higher-energy cis-FA conformer is prepared by vibrational excitation of the ground-state trans-FA conformer. The quantum yield of the trans to cis conformational process in solid hydrogen appears about two orders of magnitude smaller than in solid argon, which is explained by efficient coupling of the vibrationally excited trans form with the host vibrations deactivating the conformational change. The trans to cis conformational process is efficiently promoted by excitation of the hydrogen-matrix rovibrational transitions (host excitation), which confirms the strong coupling between vibrations of the host and embedded molecule. These results demonstrate a unique process of conformational reorganization mediated by vibrational excitation of the host. The tunneling decay of the cis-FA monomer in solid hydrogen is found to be 4 times faster than in solid argon but 30 times slower than in solid neon, and this is discussed in terms of the matrix solvation effect.